1. Stating the problem: Solve the quadratic equation $0 = x^2 - 3x + 2$. 2. Formula used: The quadratic equation $ax^2 + bx + c = 0$ can be solved by factoring, completing the square, or using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. Here, $a=1$, $b=-3$, and $c=2$. We will try factoring first. 4. Factor the quadratic expression: $$x^2 - 3x + 2 = (x - 1)(x - 2)$$ 5. Set each factor equal to zero: $$x - 1 = 0 \quad \text{or} \quad x - 2 = 0$$ 6. Solve each equation: $$x = 1 \quad \text{or} \quad x = 2$$ 7. Final answer: The solutions to the equation are $x = 1$ and $x = 2$.